The purpose of this paper is to present an algebraic generalization of the traditional two-valued logic. This involves introducing a theory of automorphism algebras, which is an algebraic theory of many-valued logic having a complete lattice as the set of truth values. Two generalizations of the two-valued case will be considered, viz., the finite chain and the Boolean lattice. In the case of the Boolean lattice, on choosing a designated lattice value, this algebra has binary retracts that have the usual (...) axiomatic theory of the propositional calculus as suitable theory. This suitability applies to the Boolean algebra of formalized token models [2] where the truth values are, for example, vocabularies. Finally, as the actual motivation for this paper, we indicate how the theory of formalized token models [2] is an example of a many-valued predicate calculus. (shrink)

Employing the theory of Birkhoff polarities as a model of model theory yields an inductively defined dual structure which is a formalization of semantics and which allows for simple proofs of some new results for model theory.

This is the third of three volumes containing edited versions of papers and commentaries presented in invited symposium sessions of the Eighth World Congress of the Econometric Society. The papers summarize and interpret recent developments and discuss future directions in a wide range of topics in economics and econometrics. The papers cover both theory and applications. Written by leading specialists in their fields, these volumes provide a unique survey of progress in the discipline.

This is a set of three volumes containing edited versions of papers and commentaries presented in invited symposium sessions of the Eighth World Congress of the Econometric Society. The papers summarize and interpret recent key developments and discuss future directions in a wide range of topics in economics and econometrics. The papers cover both theory and applications. Written by leading specialists in their fields, these volumes provide a unique survey of progress in the discipline.

This is the first of three volumes containing edited versions of papers and commentaries presented in invited symposium sessions of the Eighth World Congress of the Econometric Society. The papers summarize and interpret recent key developments and discuss future directions in a wide range of topics in economics and econometrics. The papers cover both theory and applications. Written by leading specialists in their fields these volumes provide a unique survey of progress in the discipline.

This is the second of three volumes containing edited versions of papers and commentaries presented in invited symposium sessions of the Eighth World Congress of the Econometric Society. The papers summarize and interpret key developments and discuss future directions in a wide range of topics in economics and econometrics. The papers cover both theory and applications. Written by leading specialists in their fields, these volumes provide a unique survey of progress in the discipline.

This is the third of three volumes containing edited versions of papers and commentaries presented in invited symposium sessions of the Eighth World Congress of the Econometric Society. The papers summarize and interpret recent developments and discuss future directions in a wide range of topics in economics and econometrics. The papers cover both theory and applications. Written by leading specialists in their fields, these volumes provide a unique survey of progress in the discipline.

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